Data from: Using semidefinite programming to optimize unequal deployment of genotypes to a clonal seed orchard

Tree breeders must often consider the conservation of genetic diversity, while at the same time, maximizing response to selection. In the case of seed orchards, the buyer of seed wants maximum performance, while satisfying a restriction, sometimes legislated, on the diversity deployed to the forest. Optimal selection will not completely avoid kinship but rather maximize gain while imposing a constraint on average relatedness. Here, we present the application of semidefinite programming (SDP) as a flexible approach to optimize the deployment of genotypes to a clonal seed orchard. We formulate the selection problem as an SDP, where average breeding value is to be maximized, while imposing constraints on relatedness, as well as maximum and minimum contributions from each candidate. An open-source solver, SDPA, was embedded into a tool designed to make the optimization of seed orchards by SDP simple and flexible. Case studies optimizing seed orchards for Scots pine and loblolly pine illustrate how this flexibility can be used to impose additional constraints on the scion material available from some candidate genotypes and optimize selection even when related candidates have varying degrees of coancestry among them. Additional situations where SDP can be employed are discussed.林木育种者通常需兼顾遗传多样性保护与选择响应的最大化。就种子园而言，种子采购方既希望获得最优的造林表现，同时需满足一项有时由立法规定的约束：即部署至造林林地的繁殖材料需具备足够的遗传多样性。最优选择方案不会完全消除亲缘关系，而是在对平均亲缘关系施加约束的前提下最大化遗传增益。本文提出将半正定规划（semidefinite programming, SDP）作为一种灵活方法，用于优化无性系种子园的基因型部署方案。我们将选择问题建模为半正定规划问题，目标是最大化平均育种值，同时对亲缘关系以及各候选材料的最大、最小贡献比例施加约束。我们将开源求解器SDPA集成至一款专用工具中，令基于半正定规划开展种子园优化的流程变得简便灵活。以欧洲赤松（Scots pine）和火炬松（loblolly pine）的种子园优化为例，本研究展示了该方法如何在附加约束条件下开展优化：例如对部分候选基因型可提供的接穗材料数量施加约束，或在候选材料间存在不同程度共祖亲缘关系的场景下，仍可实现最优选择。本文还讨论了半正定规划可应用的其他场景。