Post hoc blocking to improve heritability and precision of best linear unbiased genetic predictions

Abstract

Single-site clonal trials were simulated with a total of 256 clones "planted" in single-tree plots with three different environmental patterns: only patches (PATCH), only gradients (GRAD), and both components (ALL). Several simulated experimental designs were analyzed (a randomized complete block design; incomplete block designs with 4, 8, 16, and 32 incomplete blocks; and a row-column design) and compared with post hoc blocking of the same designs over a randomized complete block. Additionally, two more incomplete block designs (64 and 128 blocks) were superimposed after the fact to examine extremely small blocks. To select the best fit, the performance of the log-likelihood and mean standard error of the difference (SED) were studied and compared with mean individual broad-sense heritability. Improvement in statistical efficiency (or precision) were obtained with little effort using post hoc blocking. The results from post hoc blocking were promising with negligible differences compared with predesigned local control. The post hoc best designs were row-column (for ALL and PATCH) and incomplete block with eight blocks (for GRAD). Also, mean correlation between the true and predicted values (CORR) showed a reduction in efficiency for extremely small blocks, but no reduction in the genetic variance was noted as the size of the block decreased. Both of the criteria for model selection (log-likelihood and SED) showed similar trend to mean CORR, and their use is recommended.