Abstract
A general model was derived to find a set of optimal family contributions within a single cycle of selection from populations with a strictly hierarchical structure. The model maximized genetic gain at restricted selection proportion and group coancestry, or minimized group coancestry at restricted selection proportion and genetic gain. Populations generated from single-pair/open-pollinated and nested mating designs, as special cases of hierarchical populations, were considered in order to exemplify optimal selection through numerical analyses and simulations. Numerical analyses were made with the assumption that family numbers were finite, while family sizes were infinitely large. Monte Carlo simulations generated breeding populations of finite family number and size. The contribution of a full-sib family was a function of within-family variation the breeding values of the different types of familes involved, and the constraints considered in optimization. Results concerning the optimal solutions were discussed in terms of selection intensity, group coancestry, heritability and gain.
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