(Co)variance structures for linear models in the analysis of plant improvement data

Plant improvement programs involve the evaluation of a large number of genotypes (varieties) in a series of designed experiments known as multi-environment trials (MET). The combined analysis of MET data is a complex statistical problem which requires extensions to the standard linear mixed model. The analysis must accommodate spatial correlation structures for the plot errors from each trial and appropriate genetic covariance structures. ASReml (Gilmour, Cullis, Welham & Thompson, 1998) provides a broad range of variance structures for both the errors and the random effects in a linear mixed model. The gains in statistical efficiency resulting from the use of more complex but more realistic variance structures are large. With ASReml they can be achieved at very little extra cost since the algorithm and use of sparse matrix methods ensures timely analyses. In this paper the computational strategy of ASReml will be described and some of the scope of the program will be demonstrated in the analysis of a MET data set.