Testing for nonlinear genotype x environment interactions

The responses of different genotypes to an environmental gradient are often nonlinear and nonparallel. Current tests for differential genotypic responses are based largely on linear regression models (stability analysis) or on evaluations of all quadruples for crossover interactions (COIs) from a two-way genotype x environment (G x E) table if the environments are unquantified. The objective of this study was to develop a new statistical analysis for comparing nonlinear genotypic response curves over an environmental gradient. We first conducted an investigation to find the points where the two nonparallel curves intersected. If the intersection points lie within the attainable environmental range, the two nonparallel curves involve COI; if the points lie at the boundaries or outside the attainable range, the nonparallel curves do not involve COI. We then developed statistical tests for comparing a full and a reduced model describing the two nonparallel curves. The tests were used to analyze a wheat (Triticum aestivum L.) germination test (WGT) data under the reciprocal of a linear function and a barley (Hordeum vulgare L.) cultivar trial (BCT) data under Cauchy function. The WGT analysis shows that at least one pair of cultivars involve COI over the temperature gradient, which went undetected by a previous test based on all possible quadruples. The BCT analysis revealed that 56% of 780 possible pairs of 40 genotypes differ significantly from each other, providing more insights into the patterns of complex G x E interactions. Our analysis is therefore a viable alternative to the existing procedures.