Expected efficiencies of mating designs for advanced-generation selection

Expected efficiencies of regular hierarchical, factorial, and diallel crossing designs were compared for selection of individual offspring within progeny plantings. Variations of the diallels and factorials included partial designs, use of disconnected subsets, and in factorials, unbalanced numbers between classes of parent. Calculations were done for a single trait, adapting the within- and between-family selection index of Osborne, with fixed numbers of parents (100) and total offspring (10 000). For each design type, variable numbers of crosses per parent and variable genetic parameters (heritability and level of specific combining ability) were considered. A combination of polycross and pair-cross designs was also evaluated, with alternative assumptions concerning nongenetic variance within pair-cross plantings and the number of trees that could be planted per pair cross with fixed resources. Estimated efficiencies of different designs are considered in relation to total crosses per parent, with an illustration of the contribution of different effects. Hierarchical crosses were generally inefficient, except near the limiting case of single-pair crosses; though with large specific combining ability effects, there was an efficiency optimum with several females (common parents) per male (rare parents). Polycrosses were always markedly suboptimal. Among other types of designs, efficiencies were almost identical, except with only a few crosses per parent. In that case, partial designs tended to be marginally less efficient than complete ones and diallels were marginally behind factorials. Disconnection had very little effect, provided sets could be cross-referenced. Moderate imbalance in factorials had little impact on the expected additive genetic gain. Single-pair crosses showed a slight but definite optimum, unless specific combining ability was appreciable. The combination of designs was favored by relatively large specific combining ability effects, high heritability, and cost reductions per tree in planting unreplicated pair-cross family blocks. It is potentially efficient.