Designs Involving Three-way and Four-way Genetic Crosses for Crop and Animal Breeding Programmes

Abstract

Three-way and four way crosses can be exploited as a tool for the development of commercial hybrids with traits of genetical as well as economical importance by acquiring information regarding specific combining ability (sca) effects, and this is only possible if anyhow we are able to reduce the experimentation size by developing suitable methodology. In this study, under a fixed effects model including sca effects for three-way and four-way crosses, the estimates of general and specific combining abilities have been obtained. Methods of constructing efficient designs and plans involving partial three-way and partial four-way crosses have been obtained for a wide range of parametric combinations. The information matrices, average variance factors, efficiency factors and degree of fractionation have been derived. Also, method of constructing efficient partial three-way cross plans based on Incomplete Block Designs (IBD) with low degree of fractionation for comparing test lines with single control line has been developed. The average variance factor pertaining to estimated contrasts of general combining ability (gca) effects of half parents as well as full parents for test versus test lines and test versus control line comparisons has been calculated. Moreover, method of constructing Augmented Partial Four-way Cross (APFC) plans for comparing primary Vs. primary, primary Vs. secondary and secondary Vs. secondary lines has been developed. The information matrix related to gca effects has been also derived. All the developed class of three-way and four-way designs as well as plans are efficient and having low degree of fractionation making those suitable for experimentation with limited resources. Finally, user friendly SAS codes are written for every class of designs and plans obtained here for three-way and four-way cross experiment to compute canonical efficiencies, average variance factors etc.