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 effect s of genotype-by-environment (G x E) interaction in multi-environment testing of genotypes in plant breeding programs, there has been substa ntial development in the area of analytical methodology to quantify an d describe these interactions. Three major areas where there have been developments are the analysis of variance, indirect selection, and pa ttern analysis methodologies. This has resulted in a wide range of ana lytical methods each with their own advocates. There is little doubt t hat the development of these methodologies has greatly contributed to an enhanced understanding of the magnitude and form of G x E interacti ons and our ability to quantify their presence in a multi-environment experiment. However, our understanding of the environmental and physio logical bases of the nature of G x E interactions in plant breeding ha s not improved commensurably with the availability of these methodolog ies. This may in part be due to concentration on the statistical aspec ts of the analytical methodologies rather than on the complementary re solution of the biological basis of the differences in genotypic adapt ation observed in plant breeding experiments. There are clear relation ships between many of the analytical methodologies used for studying g enotypic variation and G x E interaction in plant breeding experiments . However, from the numerous discussions on the relative merits of alt ernative ways of analysing G x E interactions which can be found in th e literature, these relationships do not appear to be widely appreciat ed. This paper outlines the relevant theoretical relationships between the analysis of variance, indirect selection and pattern analysis met hodologies and their practical implications for the plant breeder inte rested in assessing the effects of G x E interaction on the response t o selection. The variance components estimated from the combined analy sis of variance can be used to judge the relative magnitude of genotyp ic and G x E interaction variance. Where concern is on the effect of l ack of correlation among environments, the G x E interaction component can be partitioned into a component due to heterogeneity of genotypic variance among environments and another due to the lack of correlatio n among environments. In addition, the pooled genetic correlation amon g all environments can be estimated as the intraclass correlation from the variance components of the combined analysis of variance. Where G x E interaction accounts for a large proportion of the variation amon g genotypes, the individual genetic correlations between environments could be investigated rather than the pooled genetic correlation. Indi rect selection theory can be applied to the case where the same charac ter is measured on the same genotypes in different environments. Where there are no correlations of error effects among environments, the ph enotypic correlation between environments may be used to investigate i ndirect response to selection. Pattern analysis (classification and or dination) 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 com prehensive experiments which attempt to understand the nature of diffe rences in genotypic adaptation. Hence a greater focus of interest on u nderstanding the causes of the interaction can be achieved.