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OPTIMAL DESIGN FOR EARLY‐GENERATION PLANT‐BREEDING TRIALS WITH UNREPLICATED OR PARTIALLY REPLICATED TEST LINES

Some subtle difficulties in optimal design are highlighted by the example of unreplicated field trials laid out on plots with spatial errors defined by uniformity trials. There is a dual problem of the arrangement of control plots and maximizing the number of test‐line entries. A simulation study is conducted by randomizing the allocation of genotypes to the plots of four uniformity trials in accordance with the rules defining a number of competing designs. Results are summarized in terms of the ‘SE ratio’, which reflects the improvement in precision of a given design relative to a completely random design on the same plots. The definition of the SE ratio overcomes problems induced by differential shrinkage and consequent precision of test and control lines. A general result applying to all designs shows a curvilinear improvement in SE ratio with increasing error degrees of freedom of the design. The actual arrangement of check plots is of less importance than their increasing number, which contributes to increasing error degrees of freedom. Overall measures, including expected genetic gain, are used to illustrate the choice of a balance between the total number of test‐line entries and the error degrees of freedom.