Identifying Effective Design Approaches to Allocate Genotypes in Two-Phase Designs: A Case Study in Pelargonium zonale

Robust phenotypic data allow adequate statistical analysis and are crucial for any breeding purpose. Such data is obtained from experiments laid out to best control local variation. Additionally, experiments frequently involve two phases, each contributing environmental sources of variation. For example, in a former experiment we conducted to evaluate production related traits in Pelargonium zonale, there were two consecutive phases, each performed in a different greenhouse. Phase one involved the propagation of the breeding strains to obtain the stem cutting count, and phase two involved the assessment of root formation. The evaluation of the former study raised questions regarding options for improving the experimental layout: (i) Is there a disadvantage to using exactly the same design in both phases? (ii) Instead of generating a separate layout for each phase, can the design be optimized across both phases, such that the mean variance of a pair-wise treatment difference (MVD) can be decreased? To answer these questions, alternative approaches were explored to generate two-phase designs either in phase-wise order (Option 1) or across phases (Option 2). In Option 1 we considered the scenarios (i) using in both phases the same experimental design and (ii) randomizing each phase separately. In Option 2, we considered the scenarios (iii) generating a single design with eight replicates and splitting these among the two phases, (iv) separating the block structure across phases by dummy coding, and (v) design generation with optimal alignment of block units in the two phases. In both options, we considered the same or different block structures in each phase. The designs were evaluated by the MVD obtained by the intra-block analysis and the joint inter-block-intra-block analysis. The smallest MVD was most frequently obtained for designs generated across phases rather than for each phase separately, in particular when both phases of the design were separated with a single pseudo-level. The joint optimization ensured that treatment concurrences were equally balanced across pairs, one of the prerequisites for an efficient design. The proposed alternative approaches can be implemented with any model-based design packages with facilities to formulate linear models for treatment and block structures.