Phylogenetic Diversity (PD) is a measure of the overall biodiversity of a set of present-day species (taxa) within a phylogenetic tree. In Maximize Phylogenetic Diversity (MPD) one is asked to find a set of taxa (of bounded size/cost) for which this measure is maximized. MPD is a relevant problem in conservation planning, where there are not enough resources to preserve all taxa and minimizing the overall loss of biodiversity is critical. We consider an extension of this problem, motivated by real-world concerns, in which each taxon not only requires a certain amount of time to save, but also has an extinction time after which it can no longer be saved. In addition there may be multiple teams available to work on preservation efforts in parallel; we consider two variants of the problem based on whether teams are allowed to collaborate on the same taxa. These problems have much in common with machine scheduling problems, (with taxa corresponding to tasks and teams corresponding to machines), but with the objective function (the phylogenetic diversity) inspired by biological considerations. Our extensions are, in contrast to the original MPD, NP-hard, even in very restricted cases. We provide several algorithms and hardness-results and thereby show that the problems are fixed-parameter tractable (FPT) when parameterized the target phylogenetic diversity, and that the problem where teams are allowed to collaborate is FPT when parameterized the acceptable loss of diversity.

翻译：系统发育多样性（PD）是衡量系统发育树中现存物种（分类单元）整体生物多样性的指标。最大化系统发育多样性（MPD）问题旨在寻找一组（规模/成本受限的）分类单元，使该指标达到最大值。MPD是保护规划中的一个重要问题——当资源不足以保护所有分类单元时，最小化整体生物多样性损失至关重要。我们基于现实考量拓展了该问题：每个分类单元不仅需要特定的拯救时间，还具有灭绝时间——超过该时间后便无法再被拯救。此外，可能存在多个并行工作的保护团队；我们根据团队是否允许协作处理相同分类单元，研究了该问题的两种变体。这些问题与机器调度问题（分类单元对应任务，团队对应机器）高度相似，但目标函数（系统发育多样性）源自生物学考量。与原始MPD不同，我们的扩展问题即使在极严格约束下也是NP难的。我们提出了多种算法和困难性结果，从而证明：当目标系统发育多样性作为参数时，问题是固定参数可解（FPT）的；当可接受的多样性损失作为参数时，允许团队协作的问题变体是FPT的。