Analyses of half-diallel mating designs with missing crosses: Theory and SAS program for testing and estimating GCA and SCA variance components

摘要

The half-diallel mating design, particularly a series of disconnected half-diallel mating design has been widely adopted as a mating design in many commercially important tree species for estimating the variances of general (GCA) and specific (SCA) combining abilities, heritability, and genetic correlation. Standard commercial statistical packages do not allow direct specification of the half-diallel model and therefore are not able to analyse the diallel mating design even for a balanced diallel mating structure (no missing crosses). Published special computer programs for diallel analyses do not provide an adequate solution for GCA and SCA variance components with hypothesis testing for half-diallel mating designs with missing crosses. This paper presents the theory of the method of fitting constants for analysing half-diallel mating designs with or without missing crosses. A SAS computer program (DIARANDM.SAS) for testing hypotheses and estimation of GCA and SCA variance components is developed. The program accommodates multiple variables, multiple environments, environment by GCA and environment by SCA interactions as well as data imbalance (e.g. unequal number of observations among cells and missing cells). The DIARANDM.SAS output includes (1) hypothesis testing for variance components of GCA, SCA and all interaction effects, (2) estimate of GCA, SCA and all interaction variances, (3) estimate of standard error for GCA and SCA and all interaction variance components, and (4) variance and covariance matrix for computing genetic correlations and other genetic and environmental parameters. Two examples are given to demonstrate the use of the program.