Analysis of half-diallel mating design with missing crosses: Theory and SAS program for testing and estimating GCA and SCA fixed effects

The half-diallel mating design, particularly a series of disconnected half- diallels has been widely adopted as a mating design for estimating genetic parameters and for future selection in many commercially important tree spe cies. Standard commercial statistical packages do not allow direct specific ation of the linear model associated with the half-diallel design and there fore are not capable of analysing diallel mating designs, even for balanced diallel matings (no missing crosses). Published special computer programs for diallel analyses do not provide an adequate solution for GCA and SCA fi xed effects in diallels with missing crosses. This paper presents the lease squares theory for analysing half-diallel mating designs with missing cros ses, and a SAS computer program (DIAFIXED.SAS), developed to test the signi ficance of GCA and SCA effects and estimate the GCA and SCA fixed effects. The program is flexible enough to accommodate different number of parents, multiple environments and missing individual trees as well as missing whole plots. The DIAFIXED.SAS output includes (1) hypothesis testing for GCA and SCA fixed effects and environmental effects, (2) estimates of GCA and SCA fixed effects, (3) estimates of standard errors of GCA and SCA fixed effect s. Results from a 6 by 6 half-diallel for radiata pine planted in two sites are also presented. for radiata pine planted in two sites are also present ed.