Selection in several environments by BLP as an alternative to pooled anova in crop breeding

Plant breeders often carry out genetic trials in balanced designs. That is not always the case with animal genetic trials. In plant breeding is usual to select progenies tested in several environments by pooled analysis of variance (ANOVA). This procedure is based on the global averages for each family, although genetic values of progenies are better viewed as random effects. Thus, the appropriate form of analysis is more likely to follow the mixed models approach to progeny tests, which became a common practice in animal breeding. Best Linear Unbiased Prediction (BLUP) is not a "method" but a feature of mixed model estimators (predictors) of random effects and may be derived in so many ways that it has the potential of unifying the statistical theory of linear models (Robinson, 1991). When estimates of fixed effects are present is possible to combine information from several different tests by simplifying BLUP, in these situations BLP also has unbiased properties and this lead to BLUP from straightforward heuristics. In this paper some advantages of BLP applied to plant breeding are discussed. Our focus is on how to deal with estimates of progeny means and variances from many environments to work out predictions that have "best" properties (minimum variance linear combinations of progenies' averages). A practical rule for relative weighting is worked out