When a seed produced by a single-cross (SC) maize hybrid is sown, the resulting grain yield is usually lower than that of the hybrid due to the inbreeding generated. However, if a seed from a mixture of hybrids were sown instead, the synthetic variety thus formed () would have a lower inbreeding coefficient () and a higher grain yield. The grain yield , the finite number of representatives of each parent SC () and the inbreeding coefficient of the parent lines of the SCs () are related to the . In addition, randomness and the finite size of can cause the loss of genes and genotypes and increase the . The objectives of this study were to derive formulas for (1) expressing in terms of , , and , and (2) calculating the probability of the occurrence of gene and genotype loss. It was found that for the probability of no genotype being missing from the progeny representing a parent to be at least 0.95, it is necessary that . It was also found that a sample size of 7 is sufficient for to stabilize, more visibly as is larger, and for the probability of the occurrence of erosion to be practically zero.
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