Find in Library

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 <i>s</i> hybrids were sown instead, the synthetic variety thus formed (<i>Syn_SC</i>) would have a lower inbreeding coefficient (<i>FSyn_SC</i>) and a higher grain yield. The grain yield <i>s</i>, the finite number of representatives of each parent SC (<i>m</i>) and the inbreeding coefficient of the parent lines of the SCs (<i>F</i>) are related to the <i>FSyn_SC</i>. In addition, randomness and the finite size of <i>m</i> can cause the loss of genes and genotypes and increase the <i>FSyn_SC</i>. The objectives of this study were to derive formulas for (1) expressing <i>FSyn_SC</i> in terms of <i>m</i>, <i>F</i>, and <i>s</i>, 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 <i>m</i> ≥ 15. It was also found that a sample size of 7 is sufficient for <i>FSyn_SC</i> to stabilize, more visibly as <i>F</i> is larger, and for the probability of the occurrence of erosion to be practically zero.