CLASSIFICATION OF MAIZE S-2 FAMILIES USING BICRITERIA LINEAR-PROGRAMMING

Plant breeders often use subjective ratings to describe the overall va lue of genotypes. Frequently the rating is a function of two or more a gronomic traits. Linear programming can be used to detect patterns amo ng values of agronomic traits used to make subjective ratings. The goa l of this research a-as to develop a linear programming model for use in identifying patterns among traits considered when assigning subject ive ratings to maize families and to establish classification rules ba sed on those patterns. Three traits, grain yield, moisture of grain at harvest, and percent erect plants, for 100 S-2 families of maize were considered. The 100 families were subjectively rated from one to nine , with families rated one having greatest overall utility and families rated nine having least overall utility. Using bicriteria linear prog ramming, a utility function was obtained from multiple trait data and assigned ratings, with the relative weights of yield, moisture, and er ect plants being 1.000, -0.717, and 0.724. Boundaries of utility value s were obtained for each of nine classes corresponding to each of the nine original ratings. Reclassification using boundaries of the nine c lasses resulted in some changes of number of families within classes, compared to number of families subjectively assigned to corresponding ratings, particularly for the extreme Classes 1 and 9. Class 1 contain ed four families compared to six families which received the highest r ating of one, while Class 9 contained eight families compared to thirt een families which received the lowest racing of nine. The bicriteria linear programming model did not require prior information from correc tly classified members, nor the covariance structure of the traits upo n which the original rating was based, an advantage of the model over the more widely used techniques of discriminate and classification ana lysis.