Optimum number of crosses and progeny per cross in breeding self-fertilizing crops. III. Economic constraints

Abstract

The optimum number of crosses and progeny per cross in breeding self-fertilizing crops are determined by an approach based on maximization of selection response. The total selection response is obtained by adding the individual responses from the two steps of selection: selection between crosses and selection within crosses. Optimum numbers and sizes of crosses are determined by testing capacity, number of selected crosses, number of selected lines from each selected cross, heritability, and the ratio of cost per line and cost per cross. In the case ‘selection of the best line out of the best cross’, the optimum number of crosses (1) exhibits maxima for increasing heritabilities (for any given fixed cost ratio and any total testing capacity), (2) increases with increasing total testing capacity (for any given fixed cost ratio and any heritability), (3) increases with increasing cost ratio (for any given fixed heritability and any total testing capacity), and (4) are larger for the calculation without cost constraints than for the calculation with cost constraints.