Augmented quasi-sudoku designs in field trials

Augmented designs play an important role in early-generation plant breeding when many varieties are tested and sufficient seeds are unavailable to permit each variety to be replicated more than once. The key idea is to include some replicated varieties to adjust for environmental heterogeneity and provide a good estimate of error. The simplest form of augmented design is constructed using randomized complete blocks for a few replicated varieties and augmenting each block with unreplicated varieties. This idea is readily extended to incomplete-block designs and row-column designs. A challenge is to ensure good coverage of the experimental field with replicated varieties. A problem with augmented row-column designs is that replicated variety plots may be clustered in parts of the field. One way to improve the evenness of replicated variety plot distribution is to use regions as a third blocking factor, formed by intersection of row groups (i.e. groups of adjacent rows) and column groups (i.e. groups of adjacent columns). First, a strategy to identify the numbers of regions, row groups, and column groups is proposed. Second, a general approach to search for augmented designs with three blocking factors for any numbers of unreplicated varieties and replicated varieties is presented. Finally, the algorithm is illustrated for common scenarios in plant breeding.