Using branch-and-bound algorithms to optimize selection of a fixed-size breeding population under a relatedness constraint

Tree breeders often face the challenge of conserving genetic diversity, while at the same time maximizing response to selection. When selecting advanced-generation breeding populations, the best-performing candidates will quite often be closely related and selecting them without consideration of their relatedness will very quickly erode genetic diversity. Optimal selection will not completely avoid kinship, but rather maximize gain while imposing a constraint on average relatedness. Genetic contributions are most easily optimized if breeders can manage a real, continuous distribution of contributions from parents. While generally possible when establishing seed orchards, unequal contributions to a breeding population may present difficult and time-consuming operational constraints. In these situations, a specified number of parents contributing equally may be a preferred configuration for the breeding population. Here we formulate the selection of a fixed-size breeding population while ...