Maximizing Phylogenetic Diversity under Time Pressure: Planning with Extinctions Ahead

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.