Optimum number of crosses and progeny per cross in breeding self-fertilizing crops .1. General approach and first numerical results

Based on maximization of selection response, PeSek (1986) proposed methodology for determining the optimum number of crosses and progeny per cross in breeding self-fertilizing crops. By this method the total selection response is obtained by adding the individual responses from the two steps of selection: selection between crosses and selection within crosses. In this paper, PeSek's approach has been generalized for finite or nonnormal populations. Optimum numbers of crosses are determined by testing capacity, number of selected crosses, number of selected lines from each selected cross, and heritability. In the case 'selection of the best line from the best cross', the optimum number of crosses increases monotonically with increasing testing capacity (for any given fixed heritability). For increasing heritabilities, however, the optimum number of crosses exhibits relatively flat maxima (for any given fixed testing capacity). These maxima are located at intermediate or sub-intermediate heritabilities. For varying numbers of selected crosses and selected lines from each selected cross the main results are: The optimum number of crosses i) increases with increasing testing capacity, ii) increases with increasing number of selected crosses and iii) decreases with increasing number of selected lines from each selected cross.