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Consideration of Nonparametric Approaches for Assessing Genotype-by-Environment (G × E) Interaction with Disease Severity Data

Determination of host genotype-by-environment (G × E) interaction is needed to assess the stability of cultivar traits such as plant disease resistance and to reveal differences in aggressiveness or virulence of pathogen strains among locations. Here we explored the use of rank-based methodology to quantify the concordance (or discordance) of disease responses of host genotypes across environments, based on the Kendall coefficient of concordance (W) and ancillary test statistics, in order to determine the extent to which environment affected rankings of genotypes. An analysis of four data sets for disease severity of gray leaf spot of maize (with genotypes planted in as many as 11 locations in a given year) revealed highly significant concordance (P ≤ 0.001) overall, indicating that genotypes varied little in within-environment rankings. This suggests that the G × E interaction was small or nonexistent (in terms of rankings). A novel rank-based method by Piepho was evaluated to further elucidate the interaction (if any) through a test for variance homogeneity. The Piepho test statistic was not significant (P > 0.25) for any of the gray leaf spot data sets, confirming the stability of genotypes across environments for this pathosystem; however, analysis of published data sets for other pathosystems indicated significant results. The relationship shown by Hühn, Lotito, and Piepho between the ratio of genotype and residual variances of the original data and the rank-based W statistic was evaluated using Monte Carlo simulations. A more general functional relationship was developed that is applicable over a wide range of number of genotypes and environments in the analyzed studies. This confirms previously shown linkages between rankings of genotypes within environments and variability in the original (unranked) data, thus permitting ease of interpretation of parametric and nonparametric results.