Efficiency of check-plot designs in unreplicated field trials

Check-plot designs have a lower selection intensity than unreplicated non-check-plot designs if both the number of test lines to be selected (s) and of total plots in the trial (N) are kept constant. For a check-plot design to be more efficient, local control must effectively reduce the plot error variance and increase heritability to such a level that it compensates for the corresponding loss in selection intensity and makes the expected gain from selection at least equal to that in the non-check-plot design. To realize this goal, the required minimum reduction in plot error variance in a checkplot design (relative to that in a non-check-plot design) depends on (1) check-plot frequencyf _c , (2) fractionk = s/N, and (3) ratiow ₀= ₀ ² / _g ² of non-check-plot design plot error variance ₀ ² to genetic variance _g ² among test lines. Lowerw ₀ and higherf _c andk are found to require a relatively higher reduction in plot error variance in check-plot designs. A condition is derived to show when a check-plot design may never be more efficient.