Genetic Stability and Inbreeding in a Synthetic Maize Variety Based on a Finite Model

A synthetic variety (SV) of maize may not become stable if the sample size representing each parental line (m) is small. This research aimed to evaluate the effect of m on the inbreeding coefficient (IC) of the SV (FSynL) and on the stability of its genetic constitution. An SV formed by randomly mating l unrelated lines whose inbreeding coefficient is F was considered, and a random sample was taken from the genotypic array of the progeny produced by selfing a parental line A1A2 (GA) This sample was visualized as a set of g groups of four plants whose genotypes are all four of the GA and e represented the number of plants that failed to form a group. The ICs of the selfings and those of the intragroup and intergroup crosses were calculated to derive the formula for FSynL in terms of m,g,e,l and F. It was found that as m grows, FSynL tends to (1+F)/2. With m=15, FSynL is practically stabilized and the probability of no genotype loss is 0.979. Moreover, the probability of losing A1 or A2 is practically equal to zero from m=6 onwards. However, the probability that their frequencies remain the same decreases as m gets larger.