RELATIONSHIPS BETWEEN GENOTYPE X ENVIRONMENT INTERACTIONS AND RANK ORDERS FOR A SET OF GENOTYPES TESTED IN DIFFERENT ENVIRONMENTS

Multilocation trials in plant breeding lead to cross-classified data s ets with rows = genotypes and columns = environments, where the breede r is particularly interested in the rank orders of the genotypes in th e different environments. Non-identical rank orders are the result of genotype x environment interactions. Not every interaction, however, c auses rank changes among the genotypes (rank-interaction). From a bree der's point of view, interaction is tolerable only as long as it does not affect the rank orders. Therefore, the question arises of under wh ich circumstances does interaction become rank-interaction. This paper contributes to our understanding of this topic. In our study we empha sized the detection of relationships between the similarity of the ran k orders (measured by Kendall's coefficient of concordance W) and the functions of the diverse variance components (genotypes, environments, interaction, error). On the basis of extensive data sets on different agricultural crops (faba bean, fodder beet, sugar beet, oats, winter rape) obtained from registration trials (1985-1989) carried out in the Federal Republic of Germany, we obtained the following as main result : W is-approximately-equal-to sigma(g)2/(sigma(g)2 + sigma(v)2) where sigma(g)2 = genotypic variance and sigma(v)2 = sigma(ge)2 + sigma(o)2/ L with sigma(ge)2 = interaction variance, sigma(o)2 = error variance a nd L = number of replications.