Inbreeding and Genetic Erosion from a Finite Model of a Synthetic Formed with Single Crosses.

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