Genetic Instability of a Conventional Synthetic Variety.

Synthetic varieties (SVs) such as those of maize (Zea mays L.), onion (Allium cepa L.), etc., have been supposed to be genetically stable populations through generations.  However, randomness of the genetic mechanism and the finite sample sizes of the individuals that represent each parent of a SV may cause gene loss even during the variety development and thereby affect the genotypic array expected in terms of the parental line characteristics and the Hardy–Weinberg law.  To study this issue, the number of non identical by descent (NIBD) genes in the sample of m plants of each parent was considered as a random variable (Ym).  The objectives were: 1) to determine the mean and variance of Ym, and 2) to determine the average change of the number of NIBD genes that may occur from a parent to the sample that represents it; this difference is the loss of NIBD genes of a parent.  Parents were assumed unrelated and their inbreeding coefficient was F.  It was found that the mean and variance of Ym are 2–F^m and F^m(1–F^m), respectively, and that the average loss of NIBD genes is F^m.  These results imply that for 0 ≤ F < 1 the NIBD gene loss is larger as m is smaller and F increases; with F < 1 the mean tends to 2 as m is larger, whereas the variance and gene loss tend to 0, more rapidly as F is smaller; with F = 0.25, 0.50, and 0.75, the loss of NIBD genes is near to 0 when m is 4, 8, and 20, respectively.  Finally, if the parents are pure lines (F = 1) their NIBD genes will never be lost since each parent always contributes to its sample the same and only NIBD gene of its homozygous genotype.