Inbreeding and Yield Prediction in Synthetic Maize Cultivars Made with Parental Lines: I. Basic Methods

Yield of synthetic cultivars is determined by their inbreeding, besides other factors. In turn, the inbreeding depends on the number of parents, their inbreeding, and the coaneestry among them. Previous studies have not considered the number of individuals per parent, which has an effect on the inbreeding of the synthetics and thus on their yield. A method of calculation of the inbreeding coefficient in the first and second generation of a syntheticultivar made with parental lines is presented. The inbreeding coefficients in the two generations vary inversely with n , the number of lines, and m , the number of plants per line. The inbreeding coefficient in the second generation is the same whether the first generation is obtained by intererossing the lines or by randomly mating the plants from a seed bulk of the lines. Thus, the yield prediction of the two synthetic populations is the same. Wright's formula for predicting inbreeding in a synthetic cultivar is valid only when homozygous parents are used either as single plants or as lines. If other factors that determine yield (e.g., gene frequency, imbalance in the crossing in the first and second generations of synthetic development, multiallelism and epistasis) are excluded, then, for the same level of inbreeding, synthetics are expected to yield more when using parentalines than when using individual parental plants.