On two-stage analysis of multi-environment trials

Two-stage analysis methods are often used in multi-environment trials (MET) for plant variety selection, when a single-stage approach is not feasible or too time consuming. In any two-stage analysis, the estimated effects taken to stage two must be unbiased for the effects of interest, and this means using best linear unbiased estimates based on a model with fixed genetic effects. The error (or weights) associated with the estimates must also be taken to stage two. These weights are functions of unknown variance parameters that need to be estimated at stage one. These parameters may be better estimated if genetic effects are taken as random, but resulting predicted genetic effects are biased. The bias can be removed by so-called de-regression in animal sciences. The proper weights involve a block diagonal matrix with blocks corresponding to environments, whereas diagonal weights were originally proposed in animal sciences. Two MET experiments, one fully replicated and one with partial replication of varieties, were used to compare one-stage and two-stage approaches. The results were similar, but using a full weight matrix for two-stage methods was superior to using diagonal weights. A small simulation study for trials with partial replication showed that fitting random genetic effects, de-regressing, and using a full weight matrix, was very similar to a one-stage analysis, and was superior to starting with fixed genetic effects at stage one. The use of diagonal weights was found to be very poor.