Expected Inbreeding with Recurrent Selection in Maize: I. Mass Selection and Modified Ear‐To‐Row Selection

Maize breeders reduce inbreeding either by increasing the number of selected units or by intermating unrelated selection units. To determine optimal sample size for selection, one needs explicit functions to estimate the expected inbreeding in recurrent selection. The objectives of this study were to develop functions for mass (MS) and modified ear‐to‐row selection (METRS) in maize ( Zea mays L.). By considering the number of half‐sib families and the number of plants per family, the initial inbreeding of the base population, and the intraand inter‐family coancestries, I obtained a basic equation to calculate in breeding. Knowledge of the basic population origin permitted me to extend inbreeding and coancestries of this population to any randomly mated advanced cycle of selection. Then the actual number of plants in the selection plot was transformed into the variance effective number for MS and METRS, proposed for sampling half‐sib families from an open‐pollinated population. The actual number of plants was also transformed into inbreeding effective number proposed for absence of selfing in both MS and METRS, and proposed for different numbers of males and females in METRS. Since the variance effective population size is a function of selection pressure, it was possible to obtain a general equation that included the numbers of sampled families, plants per family, and selected plants for any cycle of selection. for commonly used numbers of families, and plants per family,and selection pressures, inbreeding due to fixation by the variance effective number was very low; less than 7% for both selection methods even with 100 cycles of selection.