Effective family number following selection with restrictions

Formulations for calculations of effective number following directional selection from populations of unrelated families were developed. Two types of restrictions were considered: a maximum number of selections per family and a maximum number of families from which selections were considered. The following selection methods were studied: between-family, within-family, individual, and combined-index selections. Formulations were derived for both infinite and finite family number and size. Predicted effective number was investigated as a function of selection intensity, restriction intensity, heritability, and selection method for large populations as well as exemplifying small populations. A restriction on the number of selections per family increased the effective number, while a restriction on family number decreased the effective number. The effect of a restriction became large when the restriction was strong. The number of initial families required for obtaining a desired effective number after selection was calculated. Sometimes high family number would be required.