Enhanced heritabilities and best linear unbiased predictors through appropriate blocking of progeny trials 1

In a recent article in the Canadian Journal of Forest Research (Ericsson 1997) discussed the use of postblocking in the analysis of progeny trials. We would like to comment on three aspects of this paper: The idea of postblocking a trial is well known and has been used to advantage by Patterson and Hunter (1983) as a means of studying the nature of spatial variation at trial sites. A more detailed assessment of postblocking was carried out by Ainsley et al. (1987) who supported earlier views that " the technique is not without problems. " For example, Pearce (1983, p. 294) has warned that estimates of error may be biased with postblocking. We strongly recommend that designed experiments be used in the first instance. This is particularly the case since suitable incomplete block and row–column designs are available for a wide variety of field conditions. The power and availability of modern computers have encouraged the development of effective software packages for the generation of suitable designs for most practical situations. For example, the software package CycDesigN (http://www.ffp.csiro.au/software/) allows users to construct optimal or near-optimal experimental designs with a wide variety of options for different blocking structures, such as t-latinized designs (John and Williams 1998) and partially latinized designs (John and Williams 1999). By being able to easily generate tailor-made designs with several blocking factors to suit the particular field conditions , users are in a position to have a mechanism to efficiently control field variation; this provides a much more preferable approach than relying on the vagueness and likely inefficiency of postblocking. In his postblocking study, Ericsson used a model with fixed incomplete blocks. Such a model is suitable for situations where the field trend and, hence, the incomplete block effects are quite large. Normally, however, whilst incomplete blocks (or preferably rows and columns) are contributing to the control of field variation, the effects are not so large as to lead us to ignore the information on treatments that is contained in (or confounded with) the between-block comparisons. By specifying incomplete blocks as random, the analysis effectively provides a weighted combination of the within-block and between-block treatment information where the weights are related to the stratum residual mean squares. Then, if the incomplete blocks are not helping, the analysis reverts to one ignoring the incomplete blocks; on the other hand, if the incomplete block effects are large, the analysis corresponds …