Genetic Erosion in a Synthetic Variety Derived From Single Crosses.

Randomness, finite number of individuals, and genetic variability among those that represent each parent of a synthetic of crop species such as maize (Zea mays L.) and onion (Allium cepa L.) can cause genetic erosion during the development of a synthetic variety. This may happen when the parents are L/2 single crosses (SC_s) derived from L lines. If the inbreeding coefficient of lines (F_L) is less than 1, and the number (m) of plants that represent each SC is small, the number of non identical by descent (NIBD) genes which are contributed by two lines to their SC is a random variable (Xm). The objectives of this study were to determine:  1) the mean of Xm [E(X_m)],  2) the variance of Xm [Var(X_m)], and  3) the number of NIBD genes lost in the derivation of each SC. It was found that E(X_m) = 2 + [2 - (1/2)^m-2](1 - F_L). In addition, the average loss of NIBD genes was (1/2)^m-2(1 - F_L)   and Var(X_m) = [2 ^m+2 – 8](1 - F_L)²  / 4^m. These two results imply that when lines are pure (F_L=1), the loss of NIBD genes and the instability of the number of these genes reach their minimum (zero), and approach to it from m = 8 on, more rapidly as F_L is larger.