An optimization method for the identification of minimal sets of discriminating gene markers: application to cultivar identification in wheat

A potentially large number of molecular markers are available for identifying genotypes in various species. For wheat, cultivar identity is an important determinant for end-use segregation and for payment of end-point royalties and grower premiums. A number of dominant DNA markers, that give either a positive or negative response, have been developed previously for wheat cultivar identification. This paper gives a method for identifying minimal marker sets for a given cultivar group, for example those grown in a specific geographical zone. It is based on an integer linear programming formulation of the problem, and can find all minimal marker sets for the group if required. The paper then describes the production of two software packages, GGDS and GGIP, that incorporate this methodology. Various practical issues are also discussed. These packages enable the rapid selection of minimal marker sets for the efficient discrimination of any sample set where the marker responses of the samples are known. They are already being used by the Australian wheat industry.