Demand-Driven Technologies for Sustainable Maize ... - IITA

922Table 3: Average proportion of the interaction variation explained ( ˆR ) whentwo environment index vectors are used in AMMI model for theanalysis data set consisting of 40 genotypes and 9 environments(subset of the CIMMYT ISWYN data for 1967–1968).Target Set Self Index Complement Index Mandel’s Simulation1–41–51–81–101–20695852494338363433246154413930Mean 54 33 45wheat nursery yield trials (ISWYN) conducted by the InternationalMaize and Wheat Improvement Centre, Mexico (CIMMYT) in 1967–1968. The cultivars represented the principal types of spring wheatgrown throughout the world. Their parentage, origin and aspects oftheir agronomic characters, disease resistance and quality have beendescribed by Mackenzie et al. (1971). The trials, which consisted of40 genotypes, were conducted in 45 environments (9 out of the45 environments were analysed in this section) using a randomisedcomplete block design with three replications. The set of 40 genotypesby 9 environments by 3 replications was randomly split into 10 targetsets of 4 genotypes by 9 environments by 3 replications each (4 x 9x 3 data matrix), and the two index vectors were estimated for eachof the ten target sets as explained in the previous section. Thus, forthe analysis based on the complement index vector, a target set offour genotypes was analysed using an index vector estimated from36 genotypes x 9 environments x 3 replications. For each target set,the proportion of the interaction variation explained from regressingeach genotype’s vector of the residual interaction matrix on eachof the corresponding environment index vector was calculated and2the average ˆR value was computed for the set of ten target sets.The analysis was repeated for different target sets of sizes 5, 8, 10 and20 genotypes. The performance data of the two index vectors in terms2of ˆR values are presented in Table 3. The last column of Table 3 listsexpected ˆR 2 values for corresponding target set sizes for Mandel’ssimulation (Mandel, 1971), which may be read directly from Mandel’s2tables. If we compare average ˆR values based on the Self-indexvector with corresponding values from Mandel’s simulated valuesfor the fi ve different target set sizes, then there is invariably goodevidence that the interaction is not zero. This evidence points to theconclusion that there are almost always strong indications of genotype× environment interactions.