Genetic stability of a synthetic variety

Abstract

Synthetic varieties (SVs) have been assumed to be genetically stable populations through generations. However, it has been recognized that the randomness of the genetic mechanism, the presence of parents with heterozygous genotypes, and the finite sample sizes of the individuals that represent each parent of a SV may cause gene loss, which may make it difficult to obtain the expected genotypic array of a given SV. To study this issue, the number of non-identical by descent (NIBD) genes in the sample of m plants of each parental line was considered as a random variable (Ym). The objectives were: (1) to determine the mean [E(Ym)] and variance[Var(Ym)] of Ym, and (2) to calculate the average loss of NIBD genes of each parent (Δ_NIBD). Parents were assumed unrelated and their assumed inbreeding coefficient was F. It was found that E(Ym) and Var(Ym) were 2–F^m and F^m(1–F^m), respectively, and that Δ_NIBD was F^m. Evidently this gene loss was larger as m was smaller and F increased when F < 1. Furthermore, if F < 1 the mean tended to 2 as m was larger, whereas the variance and gene loss tended to 0. Finally, if parents are pure lines (F=1) or m is large, Var(Ym) and Δ_NIBD reduce to 0.