Here we present the strategy that achieves the lowest possible rate of inbreeding (DeltaF) for a population with unequal members of sires and dams with random mating. This new strategy results in a DeltaF as much as 10% lower than previously achieved. A simple and efficient approach to reducing inbreeding in small populations with sexes of unequal census numbers is to impose a breeding structure where parental success is controlled in each generation. This approach led to the development of strategies for selecting replacements each generation that were based upon parentage, e.g., a son replacing its sire. This study extends these strategies to a multigeneration round robin scheme where genetic contributions of ancestors to descendants are managed to remove all uncertain tics about breeding roles over generations; i.e., male descendants are distributed as equally as possible among dams. In doing so, the sampling variance of genetic contributions within each breeding category is eliminated and consequently DeltaF is minimized. Using the concept of long-term genetic contributions, the asymptotic DeltaF of the new strategy for random mating, M sires and d dams per sire, is phi/(12M), where phi = [1 + 2((1)/(4))(d)]. Predictions were validated using Monte Carlo simulations. The scheme was shown to achieve the lowest possible DeltaF using pedigree alone and showed that further reductions in DeltaF below that obtained from mating arise from preferential mating of relatives and not front their avoidance
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