Clustering genotypes based on G x E interaction in the absence of homogenecity of error variances

Abstract

A distance function between every pair of genotypes which measures the genotype-environment interaction in the case of heterogeneity of error variances in different environments was derived herein. A dissimilarity index for any set of genotypes which also measures the within group genotype-environment interaction sum of squares in terms of the pairwise distance function was also derived. Two methods of clustering, viz., statistical clustering and clustering by minimisation of average within cluster genotype-environment interaction making use of the proposed dissimilarity index were also proposed. Statistical clustering helps to group the genotypes such that genotype-environment interaction within any group is insignificant while any addition to the cluster makes it significant. In other words the idea of statistical clustering is to identify genotypes having similar response to varying environments. A point to be noted is that all the groups formed by statistical clustering may not be non overlapping. The other procedure helps to form optimum clustering by minimising the average within cluster genotype-environment interaction using an. iterative relocation algorithm. These clustering procedures were illustraited making use of two sets of data.