Optimal Family Contributions and a Linear Approximation

Selection in a population of families was investigated in terms of family contributions. The outcome of selection can be described by the selected proportion of individuals, the genetic gain, and the effective family number. There exists an optimal selection procedure, resulting in optimal family contributions, which maximizes genetic gain at a given selected proportion and minimum effective number. Numerical analyses were made for large normally distributed populations over a range of heritabilities, selected proportions, and effective numbers. Numerical results concerning the relationship between gain and effective number, heritability, breeding strategy, and family type (half- or full-sib) were discussed. Linear deployment, where family contributions are linearly related to the family average values, is an approximation to optimal selection, which is simpler to compute. Linear deployment was shown to function well as an approximation of optimal selection over a wide range of values of selected proportion, effective number, and heritability. For some special cases the linear deployment is optimal.