A PROCEDURE FOR INVESTIGATING THE NUMBER OF GENOTYPES REQUIRED TO PROVIDE A STABLE CLASSIFICATION OF ENVIRONMENTS

The technique of classification has been used to summarise relationships among test environments, based on the way they discriminate among genotypes, in multi-environment trials. However, once environments have been grouped, at a specified truncation level, there is generally no indication of the 'stability' and hence validity of the grouping. Further, there is currently no way to determine whether or not an adequate number of genotypes was used to give a robust assessment of the similarities among the environments. A procedure is presented which allowed a determination of whether an adequate number of genotypes was used to assess similarities among the environments considered. The procedure also highlighted the effect of experimental error on environmental classifications. It was demonstrated using three genotype X environment data sets with pooled genetic correlations ranging from low to high. The process used for investigating the 'stability' of the classifications involved choosing increasing proportions of the total number of genotypes available in the data set, acid classifying the environments based on each of the resultant genotypic subsets. The grouping of environments was then investigated at a particular truncation level. The process was repeated 100 times for each sub-set size and the number of different partitions of the environments, and the frequency of each partition determined. These frequencies were compared with those that were obtained, using the same procedure, but applied to data sets (of equivalent dimensions) containing random numbers. Based on the differences between the experimental and random data an assessment of the number of genotypes necessary to provide a 'stable' classification was made. Results indicated that a 'stable' classification of environments could be reached for the two data sets with moderate and high pooled genetic correlations with relatively few genotypes. However, far the data set with a low pooled genetic correlation, a 'stable' classification was not reached even when almost all of the genotypes were included. Based on the results for these three data sets the working hypothesis that the 'stability' of an environmental classification is related to the strength of the pooled genetic correlation for the data set, is advanced.